Place eggplant, peppers, carrot, zucchini, onion and garlic in 13-by-9-inch baking dish. Drizzle vegetables with oil. Roast at 400 degrees until edges are browned, 40 to 50 minutes, turning every 20 minutes. Season to taste with salt and pepper. Stir in chopped parsley.

If using leftover roasted vegetables, heat them in heavy 10-inch nonstick skillet until very hot, about 3 minutes.

Spread vegetables evenly in pan. Whisk eggs until frothy and very well-blended. Add 2 tablespoons Parmigiano-Reggiano, salt and pepper to taste. Pour eggs over vegetables and cook, without stirring, until eggs set around edges, about 5 minutes. Using rubber spatula, lift frittata edge and tilt pan slightly to allow uncooked eggs to run under cooked portion and cook until eggs are almost set in center, about 10 minutes more. Arrange mozzarella evenly over frittata top. Sprinkle with remaining tablespoon Parmigiano-Reggiano. Cover and cook until eggs are set and cheese melted, or, if preferred, place skillet under preheated broiler and broil just until frittata is set and cheese melts, about 1 minute. To serve, loosen frittata edges and slide it onto large serving platter.